Copper(II) Sulfate Pentahydrate Molar Mass Calculation

This solution explains the process of calculating the molar mass of copper(II) sulfate pentahydrate, which has the chemical formula $CuSO_4 \cdot 5H_2O$. We will use the provided atomic masses to determine the total mass of one mole of this compound.

Understanding the Chemical Formula

The chemical formula $CuSO_4 \cdot 5H_2O$ represents copper(II) sulfate pentahydrate. The dot ($\cdot$) indicates that water molecules are associated with the copper(II) sulfate compound. Breaking down the formula helps us count the number of atoms of each element:

• $Cu$: 1 atom of Copper
• $S$: 1 atom of Sulfur
• $O$: 4 atoms of Oxygen (within the $SO_4$ group)
• $H_2O$: 5 molecules of water. Each water molecule contains 2 Hydrogen atoms and 1 Oxygen atom. Therefore, the 5 water molecules contribute:
  • $5 \times 2 = 10$ atoms of Hydrogen
  • $5 \times 1 = 5$ atoms of Oxygen

Combining these, we have:

• Total $Cu$ atoms = 1
• Total $S$ atoms = 1
• Total $O$ atoms = $4 + 5 = 9$
• Total $H$ atoms = 10

Provided Atomic Masses

The calculation requires the atomic masses of each element present in the compound. The values provided are:

Step-by-Step Calculation

To find the molar mass of $CuSO_4 \cdot 5H_2O$, we sum the atomic masses of all atoms in the formula unit:

1. Mass from Copper ($Cu$): 1 atom $\times$ $63.55 \text{ g/mol} = 63.55 \text{ g/mol}$
2. Mass from Sulfur ($S$): 1 atom $\times$ $32.07 \text{ g/mol} = 32.07 \text{ g/mol}$
3. Mass from Oxygen ($O$): 9 atoms $\times$ $16.00 \text{ g/mol} = 144.00 \text{ g/mol}$
4. Mass from Hydrogen ($H$): 10 atoms $\times$ $1.01 \text{ g/mol} = 10.10 \text{ g/mol}$

Now, add the masses from all the elements together:

Molar Mass = Mass($Cu$) + Mass($S$) + Mass($O$) + Mass($H$)

Molar Mass = $63.55 \text{ g/mol} + 32.07 \text{ g/mol} + 144.00 \text{ g/mol} + 10.10 \text{ g/mol}$

Final Molar Mass Result

Adding all the values:

Molar Mass = $63.55 + 32.07 + 144.00 + 10.10 = 249.72 \text{ g/mol}$

Therefore, the molar mass of copper(II) sulfate pentahydrate ($CuSO_4 \cdot 5H_2O$) is $249.72 \text{ g/mol}$.